Show simple item record

dc.contributor.authorIsakov, Victor, 1947-
dc.contributor.authorLu, Shuai
dc.identifier.citationVictor Isakov and Shuai Lu. Increasing stability in the inverse source problem with attenuation and many frequencies. SIAM Journal on Applied Mathematics, 2018 78:1, 1-18en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractWe study the interior inverse source problem for the Helmholtz equation from boundary Cauchy data of multiple wave numbers. The main goal of this paper is to understand the dependence of increasing stability on the attenuation, both analytically and numerically. To implement it we use the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, and observability bounds for the wave equation. In particular, by using Carleman estimates for the wave equation we trace the dependence of exact observability bounds on the constant damping. Numerical examples in 3 spatial dimension support the theoretical results.en_US
dc.description.sponsorshipEmylou Keith and Betty Dutcher Distinguished Professorship and the NSF grant DMS 15-14886. The second author's work was supported by NSFC (11522108, 91630309), Special Funds for Major State Basic Research Projects of China (2015CB856003), and Shanghai Municipal Education Commission (16SG01).en_US
dc.publisherSIAM Publ.en_US
dc.relation.ispartofseriesSIAM Journal on Applied Mathematics;v.78:no.1
dc.subjectIncreasing stabilityen_US
dc.subjectInverse source problemen_US
dc.subjectExact boundary observabilityen_US
dc.titleIncreasing stability in the inverse source problem with attenuation and many frequenciesen_US
dc.rights.holder© 2018, Society for Industrial and Applied Mathematics.en_US

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record